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Planetesimal dynamics in self-gravitating discs Giuseppe Lodato IoA - Cambridge
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Summary Introduction and motivations Numerical models of gravitational instabilities (Lodato & Rice 2004, 2005) Planetesimals in self-gravitating discs (Rice, Lodato et al 2004) Planetesimal formation via gravitational instability (Rice, Lodato et al. 2006) Planetary cores dynamics in massive discs (Lodato, Britsch, Clarke 2006)
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Why planetesimals in massive discs? Massive discs? –Testi et al. (2001, 2003): In some Herbig objects, large grains: larger disc masses than previously thought (Hartmann et al 2006) –Eisner et al (2005): Massive discs in Class I objects in Taurus (M disc 0.1 - 1 M sun ) –Eisner & Carpenter (2005): Massive discs in Orion (M disc 0.1 - 0.39 M sun in 2% of source) –Clarke (2006): photoevaporation models of the ONC predicts that initially discs have to be self- gravitating
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Why planetesimals in massive discs? Why planetesimals dynamics? –Easy growth of dust up to meter sizes –Growth beyond m-sizes difficult: Sticking efficiency? (Supulver et al 1997) Migration due to gas drag (Weidenshilling 1977) –Gas rotates at sub-Keplerian speed (pressure) –To first approx., dust is Keplerian Migration time 10 3 yrs for m-size
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Evolution of massive discs Fast cooling (t cool <3 -1 ): fragmentation (Gammie 2001) Slow cooling: spiral structure, ang. mom. transport (Lodato & Rice 2004, 2005) Fundamental threshold on max. sustainable stress: 0.06 (Rice, Lodato & Armitage 2005)
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SPH simulations of planetesimals-disc interaction Intermediate-high resolution: 250,000 gas particles Heating via pdV, artificial viscosity Cooling with t cool =7.5 Disc mass: 0.25M * “ Solid ” component: 125,000 particles Interact through gravitational and drag force (single size assumed) No solid self-gravity
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Planetesimal dynamics in massive discs Gas 1000cm50cm
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Planetesimal dynamics in massive discs Collision rate highly enhanced Velocity dispersion decreases within the spiral 50 cm 1000 cm
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Rice, Lodato et al (2006) Adding the solid self-gravity Same as before, but now consider the solid self-gravity Sizes considered: 150 cm and 1500 cm Solid-to-gas ratio: 1/100 and 1/1000 Particles size: 150 cm Solid/gas ratio = 1/100 Particles size: 150 cm Solid/gas ratio = 1/1000 Particles size: 1500 cm Solid/gas ratio = 1/100
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Gravitational collapse of the solids If solid/gas ratio high enough: grav. collapse and planetesimal/core formation Typical timescale: 100 yrs ( one dyn. timescale) This is NOT the grav. inst. model for giant planet formation (a la Boss) This is NOT the Goldreich-Ward instability –No need for extremely low velocity dispersion –We find v disp 0.1c s (stirring up due to “ turbulence ” ) –Relatively large fragment mass 0.1 M Earth
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What happens next? Embryos/cores interact with the spiral structure No efficient drag for this sizes Orbital evolution of cores/embryos (Lodato, Britsch & Clarke 2006) Analogous to Nelson (2005) “ massless ” planetesimals dynamics in MRI turbulence Sizes: 100 meters (no drag) Mass: 1M Earth : no (mass dependent) Type I migration
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Orbital evolution Cores undergo “ random walk ” (cf. Nelson 2005): 10% variation of semi-major axis over the course of the run ( 100 orbits) Significant eccentricity evolution –average e 0.17 at the end of the run –Peak eccentricity: e 0.3 –cf. Nelson (2005): average e 0.05, peak e 0.1 Random walk: helps growth, prevents isolation Eccentricity growth: reduces gravitational focusing, bad for growth Possible solutions: –Coherent structure, not clear increase in vel. disp. –Direct formation of large cores (see before)
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Conclusions Solid evolution in early phases (Class I) Gas drag + structured discs: significant growth of m-sized boulders –Similar behaviour with other sources of structure in the disc (MRI - Fromang & Nelson 2005, vortices - Johansen, Klahr, Henning 2006 ) Planetesimal/core formation via fragmentation of solid sub-disc (possible growth well beyond km-sizes) Cores orbital evolution in GI (cf. Nelson 2005): –“ Random walk ” –Eccentricity growth (up to e 0.3) –Possible problem for core growth?
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